Theses and Dissertations

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Browsing Theses and Dissertations by Author "Bountis, Anastasios"

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    The Dynamics of Hamiltonian Lattices With Application to Hollomon Oscillators
    (Nazarbayev University School of Science and Technology, 2019-05-29) Zholmaganbetova, Aigerim; Bountis, Anastasios
    Many problems in theoretical physics are expressed in the form of Hamiltonian systems. Among these the first to be extensively studied were low-dimensional, possessing as few as two (or three) degrees of freedom. In the last decades, however, great attention has been devoted to Hamiltonian systems of high dimensionality. The most famous among them are the ones that deal with the dynamics and statistics of a large number N of mass particles connected with nearest neighbor interactions. At low energies E, these typically execute quasiperiodic motions near some fundamental stable periodic orbits (SPOs) which represent nonlinear continuations of the N normal mode solutions of the corresponding linear system. However, as the energy is increased, these solutions destabilize causing the motion in their vicinity to drift into chaotic domains, thus giving rise to important questions concerning the systems behavior in the thermodynamic limit, where E and N diverge with E=N = constant. One of the open problems in Hamiltonian dynamics, therefore, examines the relation between local (linear) stability properties of simple periodic solutions of Hamiltonian systems, and the more “global” dynamics. In this thesis, after reviewing the main results on these topics for the case of N-particle Fermi-Pasta-Ulam Hamiltonians, I proceed to apply the corresponding methods to a lattice of Hollomon oscillators, which are of interest to applications in problems of nonlinear elasticity.
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    Synchronization of Coupled Nonlinear Oscillators with Applications to Photonic Arrays
    (Nazarbayev University School of Science and Technology, 2019-05-01) Zharas, Banu; Bountis, Anastasios; Tourassis, Vassilios D.
    In recent years, the study of synchronization of coupled oscillators have been the subject of intense research interest, leading to many new and unexpected phenomena. Our research is first focused on the analysis of a network of coupled nonlinear oscillators exhibiting the breakdown of synchronization into fascinating “chimera states” exhibiting the coexistence of synchronized and unsynchronized parts. We then apply these ideas to laser arrays of photonic “oscillators”, which have numerous applications in optical communications, sensing and imaging. First of all, we demonstrate the occurrence of synchronization and chimera states in a simpler problem, consisting of a ring of coupled 4D simplified Lorenz systems, in which each oscillator is described by a Li-Sprott oscillator [1]. An interesting feature of each oscillator is the coexistence of a limit cycle and two symmetric strange attractors for some specific range of parameters, which influences the global synchronization dynamics and leads to the formation of chimera states. Inspired by this model, we study some fascinating oscillatory phenomena of coupled photonic oscillators consisting of dimers of semiconductor lasers, each of which is capable of performing limit cycle oscillations. Coupling in an appropriate way a large number of dimers in long arrays we find that they can exhibit combinations of oscillatory patterns involving long amplitude oscillations (LAO) and also localized oscillations of very small amplitude close to the fixed points (LOCFP). As preliminary results of this investigation, we show the coexistence of LOA and LOCFP patterns reminiscent of “chimera–like” states and LOCFP “breather– like” phenomena. Both of these behaviors are shown to be spatially robust, when we calculate the Discrete Laplacian of their amplitudes for long times.